Sufficiency-Type Stability and Stabilization Criteria for Linear Time-Invariant Systems with Constant Point Delays

Abstract

We derive a set of criteria of asymptotic stability for linear and time-invariant systems with multirate point delays. The criteria are concerned with α-stability local in the delays and e-stability independent of the delays and are classified in several groups according to the technique dealt with. The techniques used include both Lyapunov's matrix inequalities and equalities and Gerschgorin's circle theorem. Lyapunov's inequalities are guaranteed if a set of matrices built from matrices of undelayed and delayed dynamics are stability matrices. Some extensions to robust stability of the above results are also discussed.